I want to understand group theory a bit better, so I’ll be making a couple of pictures. One statement that sparks curiosity is “The only symmetric group (all permutations of N elements) that has an outer automorphism is S6.” nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqknzsux7p6lzwzdedp3m8c3c92z0swzc0xyy5glvse58txj5e9ztqaufa4k (nprofile…fa4k) and nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqt76as6gjr7pzg0taz40e55smjjegmj89ud7g056aqed90hs7cynsacyu7x (nprofile…yu7x) have already made some cool picture about this at:
https://blogs.ams.org/visualinsight/2015/08/15/tutte-coxeter-graph/
Here is an animated version of the Cremona Richmon configuration. Each point is a permutation of a pair of numbers between 1 and 6. Each of the 15 points is in a unique combination of 3 of the 15 lines. Each of the 15 lines has a unique combination of 3 points. Also, dual to the 6 numbers, there are 6 “synthematic totals”, sets of 5 disjoint lines. The 5 thick lines represent one such total, it can be rotated to produce 4 more. The 6th one is the set of all green lines.
More to come...
Gerard Westendorp
npub1a3…ngyzl
2025-04-02 09:11:18 UTC
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wss://relay.ditto.pubPublished at
2025-04-02 09:11:18 UTCEvent JSON
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"content": "I want to understand group theory a bit better, so I’ll be making a couple of pictures. One statement that sparks curiosity is “The only symmetric group (all permutations of N elements) that has an outer automorphism is S6.” nostr:nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqknzsux7p6lzwzdedp3m8c3c92z0swzc0xyy5glvse58txj5e9ztqaufa4k and nostr:nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqt76as6gjr7pzg0taz40e55smjjegmj89ud7g056aqed90hs7cynsacyu7x have already made some cool picture about this at:\nhttps://blogs.ams.org/visualinsight/2015/08/15/tutte-coxeter-graph/\nHere is an animated version of the Cremona Richmon configuration. Each point is a permutation of a pair of numbers between 1 and 6. Each of the 15 points is in a unique combination of 3 of the 15 lines. Each of the 15 lines has a unique combination of 3 points. Also, dual to the 6 numbers, there are 6 “synthematic totals”, sets of 5 disjoint lines. The 5 thick lines represent one such total, it can be rotated to produce 4 more. The 6th one is the set of all green lines.\nMore to come...\n\nhttps://media.mathstodon.xyz/media_attachments/files/114/267/569/199/275/167/original/369136dd301226c6.mp4",
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